The Dutchman travelled to Manchester On Thursday to complete personal terms and undergo a medical ahead of his move to Old Trafford.
Van Persie has now put pen to paper, putting one of the summer's longest running transfer sagas to rest.
The 29-year-old was last season's top scorer, netting 30 times as Arsenal finished 3rd in the Premier League, and picked up the PFA Players' Player and Fans' Player of the Year awards.
United faced stiff competition from rivals Manchester City and Serie A champions Juventus in their pursuit for the talismanic front-man.
Manager Sir Alex Ferguson revealed on Thursday that he hopes to have the deal completed in time for Van Persie to make his debut against Everton on Monday and is delighted to have landed his top target.
"Robin is a world-class striker with a proven record in England and in European football," he told the club's official website.
"His talents need no introduction to our fans. He has scored a number of goals against us in some classic battles with his former club. His movement, finishing and all-round ability are outstanding."
Van Persie will face competition for a starting place from Danny Welbeck, Wayne Rooney and Javier Hernandez as United look to reclaim the league title back from Manchester City.
"It's an honour to sign for Manchester United," he said.
"I am looking forward to following in the footsteps of so many great strikers, bringing my experience and playing my part to help the team compete for the biggest trophies in the game. I can't wait to get started."
